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We have the following indirect implication of form equivalence classes:

100 \(\Rightarrow\) 369 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
100 \(\Rightarrow\) 369	Communication sur les recherches de la th'eorie des ensembles, Lindenbaum, A. 1926, C. R. Soc. Sci. Lett. Varsovie

Here are the links and statements of the form equivalence classes referenced above:

Howard-Rubin Number	Statement
100:	Weak Partition Principle:  For all sets \(x\) and \(y\), if \(x\precsim^* y\), then it is not the case that \(y\prec x\).
369:	If \(\Bbb R\) is partitioned into two sets, at least one of them has cardinality \(2^{\aleph_0}\).

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